short answer, no.
the cable modems record the MAC address of the modem so that you have one cable model going to one account.
it's possible that you could have a second cable account and pay twice as much, but I don't see the point in doing that.
if you buy a second account, and second cable modem, and second router, then yes, I believe that you can just split the cable, (this is how it's done in the street as well).
However, if you just want a private network set up upstairs and a private network downstairs then you'd do better to do things slightly different.
use your existing cable feed, and cable modem.
use the first cable modem to create a stub network to connect 2 independant networks to the same internet connection.
I'll try to represent this with ascii
10.0.0.1 / \ 10.0.0.2
independant network 1 independant network 2
of course the downside there is that both your networks share the same internet bandwidth, though the two networks are completely independant of each other, and you can set up access rules on routers A and B to allow cross network traffic through the router attached to the first network.
Alternatively, you may be able to implement the same kind of thing on a good cable router.
I believe that some Linksys routers are hackable so that you can remove the factory standard web interface and run a linux distro called tomato on them that allows you to set up multiple networks independent of each other and set up QOS rules for each network so that you could give your network preferred bandwidth whilst giving a restricted bandwith to the rest of the house.
this would look like this
switch(or WAP) switch(or WAP)
the switches or WAPs, (possibly combined) may be cheaper than buying seperate routers,
and you may be able to use your existing router as a switch/wap
(of course, you'll only need a switch if you plan to use the seperate vlans over multiple machines, if it's just one computer you could just plug it straight into one of the linksys router ports).
*there may be other routers other than linksys that you can hack like this
*i've not done this, I was just talking about this at work yesterday and someone else had said that they were planning to do something like this for applying QOS to different people in and around their house.